Brewster Angle Calculator

Work out brewster angle instantly with clear inputs, formula shown and shareable results.

About Brewster Angle Calculator

At Brewster's angle, arctan(n2/n1), the reflected and refracted rays are exactly 90 degrees apart and the reflection contains no light polarised in the plane of incidence. Air to glass at 1.52 gives 56.7 degrees. This is why polarising sunglasses cut glare from water and roads so effectively.

Formulas

Brewster's angle

theta(B) = arctan(n2 / n1)

Geometry

reflected and refracted rays are perpendicular

Worked example

With the default values below, Brewster Angle Calculator returns Brewster Angle of 56.659. Change any input above and every figure here is recalculated in your browser.

Inputs used

Refractive index of the incident mediumminimum 0: 1
Refractive index of the second mediumminimum 0: 1.52

Results

Brewster Angle: 56.659 deg
Angle Of The Refracted Ray: 33.341 deg
Index Ratio n2/n1: 1.5200
Polarisation State: Reflected light is fully polarised parallel to the surface

Step by step

1Values used
2Brewster's angle
3Geometry
4Brewster Angle= 56.659 deg
5Angle Of The Refracted Ray= 33.341 deg
6Index Ratio n2/n1= 1.5200
7Polarisation State= Reflected light is fully polarised parallel to the surface

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

What is Brewster's angle for water?

About 53.1 degrees for n = 1.333, which is roughly the elevation at which surface glare is strongest and most polarised.

Why does polarised light vanish in reflection?

The dipoles set oscillating in the second medium cannot radiate along their own axis, and at Brewster's angle that axis points exactly where the reflected ray would go.